Abstract
The approximation methods for integral equations described in Chapters 11 to 13 lead to full linear systems. Only if the number of unknowns is reasonably small may these equations be solved by direct methods like Gaussian elimination. But, in general, a satisfying accuracy of the approximate solution to the integral equation will require a comparatively large number of unknowns, in particular for integral equations in more than one dimension. Therefore iterative methods for the resulting linear systems will be preferable. In this chapter, we will discuss some efficient iterative methods for solving linear systems obtained by discretizing operator equations based on the principal idea of the residual correction. In addition, at the end of this chapter we will briefly enter into the question of stability of the linear systems arising in the discretization of integral equations.
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© 1989 Springer-Verlag Berlin Heidelberg
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Kress, R. (1989). Iterative Solution and Stability. In: Linear Integral Equations. Applied Mathematical Sciences, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97146-4_14
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DOI: https://doi.org/10.1007/978-3-642-97146-4_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-97148-8
Online ISBN: 978-3-642-97146-4
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